Characterizations of Daugavet points and delta-points in Lipschitz-free spaces

A norm 1 element x of a Banach space is a Daugavet point (respectively, a Delta-point) if every slice of the unit ball (respectively, every slice of the unit ball containing x ) contains an element which is at distance almost 2 from x. We characterize Daugavet points and Delta-points in Lipschitz-free spaces. Furthermore, we construct a Lipschitz-free space with the Radon-Nikodym property and with a Daugavet point; this is the first known example of such a Banach space.